Answer:
The lower bound of a 99% C.I for the proportion of defectives = 0.422
Step-by-step explanation:
From the given information:
The point estimate = sample proportion
= 0.55
At Confidence interval of 99%, the level of significance = 1 - 0.99
= 0.01
Then the margin of error
E = 0.128156
E ≅ 0.128
At 99% C.I for the population proportion p is:
= 0.55 - 0.128
= 0.422
Thus, the lower bound of a 99% C.I for the proportion of defectives = 0.422
9514 1404 393
Answer:
maximum difference is 38 at x = -3
Step-by-step explanation:
This is nicely solved by a graphing calculator, which can plot the difference between the functions. The attached shows the maximum difference on the given interval is 38 at x = -3.
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Ordinarily, the distance between curves is measured vertically. Here that means you're interested in finding the stationary points of the difference between the functions, along with that difference at the ends of the interval. The maximum difference magnitude is what you're interested in.
h(x) = g(x) -f(x) = (2x³ +5x² -15x) -(x³ +3x² -2) = x³ +2x² -15x +2
Then the derivative is ...
h'(x) = 3x² +4x -15 = (x +3)(3x -5)
This has zeros (stationary points) at x = -3 and x = 5/3. The values of h(x) of concern are those at x=-5, -3, 5/3, 3. These are shown in the attached table.
The maximum difference between f(x) and g(x) is 38 at x = -3.
